HyperProb is a Hypercard tutoring system designed to help students develop an effective step-by-step schema for solving probability problems. With this program, students are able to select areas they wish to study via hypermedia links and develop an understanding of terminology and procedures at their own pace with continued reinforcement. Nine…

Research on the psychological processes involved in early school arithmetic has now accumulated sufficiently to make it possible to construct a coherent account of the changing nature of the child's understanding of number during the early school years. This monograph presents an account of how number concepts are extended and elaborated as a…

This issue contains abstracts and critical comments for 11 articles. Three articles focus on problem solving; the remainder concern understanding of the equals sign, mathematical structure, mathematical abilities, the role of language in tasks involving sets, sex differences in mathematical errors, subtraction, algorithms as schemes, and…

This paper describes a classroom teaching experiment conducted in three fifth-grade mathematics classrooms with students of different achievement levels. Virtual fraction manipulative concept tutorials were used in three one-hour class sessions to investigate the learning characteristics afforded by these technology tools. The virtual fraction…

Advances the idea that performance errors should contribute positively to the process of learning. Argues that errors do not occur randomly and that instructional theory should not condemn errors, but seek them. (PK)

In 1985, Indiana joined the growing list of states assessing students' achievement at various levels. During February 1985, over 63,000 third-grade students took the 40-item Indiana Basic Competency Skills Test. A mean of 34.7 was achieved. An item analysis was performed for a random sample of 6,439 students (approximately 10%). Findings confirm…

The clinical interview can be a useful individualized assessment and remedial tool for students with difficulties in arithmetic. To use it effectively, the examiner must establish rapport with the student, discover his metacognitive strategies, and determine the student's optimum ability level. (JDD)

TORUS, a prototype technology-based educational diagnostic program, is described. The usefulness of TORUS to identify and remediate the mathematics misconceptions of students with learning disabilities is reported. Results suggest the need for greater emphasis on conceptual understanding in mathematics instruction. (Author/DB)

This report describes TORUS, a computer-based program for elementary school students with learning disabilities which analyzes student work samples in addition and subtraction and provides individual profiles of student misconceptions and weaknesses. Initially, work samples from 236 middle school students with learning disabilities were analyzed…

This literature review explores the phenomenon of dysmathematics and problems in its definition. Dysmathematics is suggested as a modern term for low achievement in mathematics. This document addresses: (1) concomitant variables associated with dysmathematics; (2) mathematical characteristics of dysmathematicians; (3) diagnosis and prescription…

Knowledge about the structure of arithmetic expressions enables people to reason effectively about such expressions, including an ability to judge equivalence under transformations. This paper reports an empirical study of six middle-school children who judged the equivalence of three sets of three-term arithmetic expressions with an addition and…

An overview is presented of information processing analyses of knowledge and performance in three areas of the elementary mathematics curriculum: basic addition and subtraction facts, complex procedures such as multicolumn subtraction, and the solution of word problems. Theories of the knowledge associated with "expert" performance are discussed.…

This document was prepared to assist teachers in Virginia in three ways: (1) by assessing student achievement on the competencies adopted by the State Board of Education; (2) by diagnosing student errors in mathematics; and (3) by prescribing instructional activities designed to promote student mastery of skills assessed in the competency program.…

A theory of how people learn certain procedural skills is presented. It is based on the idea that the teaching and learning that goes on in a classroom is like an ordinary conversation. The speaker (teacher) compresses a non-linear knowledge structure (the target procedure) into a linear sequence of utterances (lessons). The listener (student)…

The objective of this paper is to explain the need for and defend the sufficiency of the child's-play method of teaching the place value notation concept to preschool and elementary school children. Discussion first illustrates error patterns of school children in the use and interpretation of place value notation, arguing that the errors reflect…